Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory

Abstract

Functionally graded material (FGM) is an in-homogeneous composite, constructed from various phases of material elements, often ceramic and metal. This work aims to examine the behavior of free vibration in porous Functionally Graded Beams (FGBs) in 2 directions (2D) by using nth-order shear deformation theory. With the help of Hamilton's principle and Reddy's beam theory, equilibrium equations for free vibration were derived. Boundary conditions such as Simply Supported – Simply Supported (SS), Clamped – Clamped (CC) and Clamped-Free (CF) were employed. A unique shear shape function was derived and nth-order theory was adapted to take into account the effect of transverse shear deformation to get zero shear stress conditions at the top and bottom surfaces of the beam. Based on power law, FGB properties were changed in length and thickness directions. The displacement functions in axial directions were articulated in algebraic polynomials, including admissible functions which were used to fulfill different boundary conditions. Convergence and verification were performed on computed results with findings of previous studies. It was found that the results obtained using the nth-order theory were in agreement and allows for better vibration analysis in a porous material.

Keywords

• free vibration behaviour
• nth order shear deformation theory
• lagrange’ s equations
• 2d fgb